# How do you find the equation of the tangent line and normal line to the curve #y = (5+6x)^2# at the point (-4,361)?

##### 1 Answer

**1) Equation of Tangent**

Step1:

The *tangent is a line* so it has the form of a line:

Also the gradient,

So,

Step2:

At the point

So,

Step3:

Putting the point

hence equation of tangent is

**Equation of normal**

The equation of normal is also a line of the same form as the tangent.

The only difference is at the level of the gradient.

We can *deduce the gradient* of the normal from the fact that the normal is a line *perpendicular* to the tangent

This implies the product of their gradients is

So let

Hence equation of normal is